pilot-wave theory

Pilot-wave theory, first sketched by Louis de Broglie in the 1920s and revived by David Bohm in 1952, restores a familiar kind of reality: particles that always have definite positions and follow definite paths. Alongside the particle there is a real wave — the wavefunction — that does not collapse but instead acts as a 'pilot', guiding the particle along according to a precise equation of motion. Nothing is left to chance in the underlying dynamics; the theory is fully deterministic.

Where, then, does quantum randomness come from? From our ignorance of the exact starting position of each particle. If those positions are distributed in the way the Born rule prescribes, then averaging over our ignorance reproduces every standard quantum prediction exactly. In the double-slit experiment, for example, each particle really does go through one slit, yet the guiding wave passes through both and steers the particles into the familiar interference pattern.

The trade made here is the reverse of many-worlds: pilot-wave theory keeps a single definite reality and a clear answer to 'where is the particle', but the wave must be a real field on a high-dimensional configuration space, and the guidance is blatantly nonlocal — what happens to one particle can depend instantly on a distant partner. That nonlocality is not a flaw smuggled in; Bell's theorem shows any theory matching quantum predictions must be nonlocal in this sense.